After a career writing songs and film scripts about his father, who went missing in action in the second world war, Pink Floyd frontman Roger Waters has returned to the theme in a new poem he presented to a 93-year-old war veteran who has solved the mystery of where his father was killed.

The British veteran, Harry Shindler, who has spent years cracking the cases of soldiers lost in Italy, received the poem from a grateful Waters after he discovered documents revealing the exact time and place where the singer's father died during a German attack, shortly after the Allied landing at Anzio in 1944.

"Waters is delighted and so am I," said Shindler from his home in Italy. "He is a man who has spent his whole life trying to find his father and now he's done it."

Waters's father, Lieutenant Eric Fletcher Waters – who died when his son was five months old – is central to Pink Floyd's The Wall, in which the disturbed protagonist, Pink, grows up longing for a father figure.

"I was very angry," Waters has said about never knowing his father. "Because he was missing in action, presumed killed, until quite recently I expected him to come home."

Shindler had never heard of Pink Floyd, but knew of Waters and decided to help him when the singer this year visited the Commonwealth war graves cemetery at Monte Cassino, where his father's name is listed.

"I read about how he didn't know his dad and I felt great affection for him," said Shindler, who also landed at Anzio and is the head of a veterans' association.

Shindler tracked down a report of fighting after the Anzio landing at the National Archives in Kew, which revealed Waters was killed in a ditch at 11.30am on 18 February 1944, after his company was surrounded during "stiff fighting". His body has never been found.

More importantly, Shindler found a map reference, which he matched with a then rural spot that is now at the centre of the town of Aprilia.

"Waters didn't know where his dad was killed, but nobody had lifted a finger," said Shindler. "I knew there had to be a war diary, but I never thought it had been kept for 70 years."

Signing it, "To Harry, with gratitude," Waters sent Shindler his poem, One River, which was published on Monday in Italy's La Repubblica and contains the lines: "My father, distant now but live and warm and strong / In uniform tobacco haze."

"I am now talking to the council in Aprilia about unveiling a plaque and holding a ceremony next 18 February, to which Waters could come," said Shindler. "He might well think his war is over now."